Leech left the FDF just before Christmas to join the British Property Federation, following almost a decade with the organisation.
Wright will take on the role before Easter. Until then, Jim Moseley, a former president of the federation, will continue as acting director general.
President of the FDF, dame Fiona Kendrick, said Wright was“ideally qualified” to champion the sector during a period of change.
“Wright’s role will be to ensure that government and stakeholders understand the importance of food and drink manufacturing, and support our industry to meet the changing needs of UK consumers in the future,” she said.
Wright was corporate relations director of drinks giant Diageo for 14 years. Before this he held roles at Mars Confectionery, Burger King, Pillsbury and Boots the Chemists.
Wright said: “It's a privilege to be asked to lead its representative body and to be its advocate in the important challenges to come.”